The simple interest on a sum of money is 1/16 of the principal and the number of years is equal to the rate per cent annum. Find the rate per cent.

Options

A. `2(1)/(2)%`
B. `3(1)/(2)%`
C. `4(1)/(2)%`
D. `9(1)/(2)%`

Answer

To solve the problem, let's break it down step by step.

### Step 1: Understand the given information
We know that:
- The simple interest (SI) is \( \frac{1}{16} \) of the principal (P).
- The number of years (T) is equal to the rate of interest (R) per annum.

### Step 2: Write the formula for Simple Interest
The formula for Simple Interest is given by:
\[ SI = \frac{P \times R \times T}{100} \]

### Step 3: Substitute the known values into the formula
From the problem, we know:
\[ SI = \frac{1}{16} P \]
And since \( T = R \), we can substitute \( T \) with \( R \) in the SI formula:
\[ \frac{1}{16} P = \frac{P \times R \times R}{100} \]

### Step 4: Simplify the equation
We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ \frac{1}{16} = \frac{R^2}{100} \]

### Step 5: Cross-multiply to solve for \( R^2 \)
Cross-multiplying gives:
\[ 100 = 16R^2 \]

### Step 6: Solve for \( R^2 \)
Dividing both sides by 16:
\[ R^2 = \frac{100}{16} = 6.25 \]

### Step 7: Find \( R \)
Taking the square root of both sides:
\[ R = \sqrt{6.25} = 2.5 \]

### Step 8: Conclusion
The rate of interest \( R \) is \( 2.5\% \).